Question

what is the value of the Fourier coefficients a0 and bn for (x)=x²;-1<x<1​

Answer 1

Answer:

bn. = 1 π. ∫. 2π f(x) sin nx dx where integrations are over a single interval in x of L = ... q Finally, specifying a particular value of x = x1 in a Fourier series,

Answer 2

I need use Fourier series of f(x)=x2+xf(x)=x2+x ,x∈(−π,π)x∈(−π,π)

to prove that ∑n≥11n2=π26∑n≥11n2=π26.

I calculated the Fourier series: x2+x=π23+∑n≥14n2(−1)ncosnx−2n(−1)nsinnxx2+x=π23+∑n≥14n2(−1)ncosnx−2n(−1)nsinnx.

And could not find any −π<x<π−π<x<π that could solve my problem.

I double-checked my calculations and could not find any problem with the series, could you please give me some hint about my error ?

I know that we can calculate ∑n≥11n2=π26